Flow of polar fluids in a circular pipe. (1st report, oscillatory flow without spin on the pipe wall).

Viscous oscillatory flow of polar fluids in a circular pipe is studied mathematically, with the following results: (i) Profiles of velocity and angular velocity, vorticity and shear stress distributions, flow rates and dissipation of energy over the cross section are obtained as exact solutions of the full first and second Cauchy's equations . (ii) For large frequencies, the amplitudes of velocity and angular velocity become small in inverse proportion to the first or second power of Wormersly number, respectively. For small frequencies, the fluid flow becomes quasi-steady. The phase lag of velocity for pressure diminishes gradually. (iii) A big size effect makes the polar fluid near-Newtonian, then the angular velocity becomes equal to half of vorticity. (iv) When the rate of vorticity viscosity to shear viscosity becomes small, the polarity of fluid diminishes and the angular velocity approaches zero. (A)